The incident took place on the A81 Callander to Blairhoyle road on Saturday, September 4.
Around 4.10pm, two motorcycles were travelling southbound on the A81 when the rider of a Blue Yamaha R6 appeared to lose control and came off the bike, landing on the northbound carriageway.
The rider of a Yellow Suzuki RGSX then collided with the rear of a black Ford Kuga, coming off the bike and landing on the southbound carriageway.
Emergency services attended and a 48-year-old woman who was travelling on the Yellow Suzuki RGSX was taken to the Queen Elizabeth University Hospital in Glasgow, where medical staff describe her condition as critical.
A 56-year-old man riding the Blue Yamaha R6 was taken to Forth Valley Royal Hospital for treatment.
Medical staff describe his condition as stable.
Police are appealing to members of the public for further information.
Sergeant John Lang, of Forth Valley Road Policing Unit, said: “Enquiries are ongoing to establish the full circumstances surrounding this incident and I would appeal for anyone with information to please get in touch.
“In particular I would like to speak to anyone who may have observed the two motorcycles involved driving along the A81 from Callander.
“I would also urge any motorists with dash-cams who were on the road to check their footage in case they have captured anything which could be of significance.
“Anyone with information is asked to contact Police Scotland through 101, quoting incident number 2284 of Saturday, September 4, 2021.”